• Organizational meeting
• Probability that random polynomial has no real roots (Talk by Anna Gusakova)
• Theorems on positive real functions (Talk by Anna Muranova)
• Non-explosion of solutions to SDEs with singular coefficients (Talk by Chengcheng Ling)
• Emergence of Flocking in the Fractional Cucker-Smale Model (Talk by Peter Kuchling)

• Introduction to partition functions
• Partition Functions and Gibbs Measures
• Correlation Functions
• Phase Transitions (Critical Exponents and Models)
• Scaling Limits

Reading Spectral graph theory by Fan R. K. Chung

• Chapter 2: Isoperimetric problems
• Chapter 3: Diameters and eigenvalues
• Talk by Anna Muranova: On effective resistance of electric network with impedances
• Talk by Melissa Meinert: Ollivier Ricci curvature for general Laplacians
• Markov chains
• Talk by Filip Bosnic: Examples of Poincaré and log-Sobolev inequalities on discrete configuration spaces
• Introduction to random graphs by Alan Frieze and Michał Karoński

Discuss Lévy Processes and Infinitely Divisible Distributions by Ken-iti Sato

• Chapter 1 (pp. 1 - 30): Examples of Levy Processes
  
• Chapter 2 (pp. 31 - 68): Characterisation and Existence of Levy Processes and Additive Processes
• Chapter 2 (pp. 31 - 41): Infinitely Divisible Processes and the Lévy-Khintchine formula
• Chapter 2 (pp. 54 - 67): Transition Functions and the Markov Property; Existence of Lévy and Additive Processes
• Chapter 3 (pp. 69 - 77): Selfsimilar and Semi-selfsimilar Processes and their Exponents
• Chapter 3 (pp. 77 - 90): Representations of Stable and Semi-stable Distributions
• Viswanathan et al. Papers: “Levy Flight Search Patterns of Wandering Albatrosses” and “Optimizing the Success of Random Searches”
• Bertoin (pp. 18-24): Potential theory: Markov property and important definitions
• Bertoin (pp. 43-48): Duality and time reversal
• Bertoin (pp. 48-56): Potential theory: capacity measure; essentially polar sets and capacity
• Bertoin (pp. 56-68): Potential theory: energy; the case of a single point
• Bertoin (pp. 71-84): Subordinators: definitions; passage across a level; arcsine laws
• Bertoin (pp. 84-99): Subordinators: rates of growth; (Hausdorff-)dimension of the range

Discuss

• Maximum principle for ecliptic operators (Gibarg-Trudinger)
• Paley-Littlewood Decomposition (Grafakos classical Fourrier Analysis, second or third edtion)
• Another looks at Sobolev spaces (Articles Brezis Bourgain_Mironescu)
• Spectral theory: spectral measure for Unbounded operators
• Spectral theory for unbounded operator and spectral measure (Book by Reed-Simon)
• Restriction of the Fourier Transform on the sphere (Book by Elias Stein)
• Interplation of Banach spaces and application (Lecture note by Alessandra Lunadri Theory of interpolation 2009)
• Introduction to optimal transport theory (Book by Cedri Villani: Old and New, it is free on-line)
• Introduction to control and non linearity (Book by Jean-Michel Coron: Control and Non-linearity free one his we-page)
• Introduction to Calculus of variations